We present various properties of nuclear and compact-star matter, comparing the predictions from two kinds of phenomenological approaches: relativistic models (both with constant and density-dependent couplings) and non-relativistic Skyrme-type inter
actions. We mainly focus on the liquid-gas instabilities that occur at sub-saturation densities, leading to the decomposition of the homogeneous matter into a clusterized phase. Such study is related to the description of neutron-star crust (at zero temperature) and of supernova dynamics (at finite temperature).
